This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A245290 #24 Jul 24 2023 04:53:18 %S A245290 1,31,5119,9961471,259577085951,94554701453852671, %T A245290 494214691850093043122175,37747948215762478445361018961919, %U A245290 42694960288928350006693371507341885702143,722273364120299921501331975953872089285372151857151 %N A245290 Number of normalized graph Laplacian matrices of nonempty labeled graphs of 2n vertices that are separable in C^2 X C^n as density matrices in quantum mechanics. %C A245290 Since separability is not invariant under graph isomorphism, all 2^(n(2n-1))-1 nonzero Laplacian matrices are treated as different. A nonzero Laplacian matrix different from the complete graph is separable in C^2 X C^n if and only if its complement is. Since the complete graph is separable, this means that a(n) is odd for all n. %H A245290 Chai Wah Wu, <a href="http://dx.doi.org/10.1016/j.physleta.2005.10.049">Conditions for separability in generalized Laplacian matrices and diagonally dominant matrices as density matrices</a>, Physics Letters A, 351 (2006), 18-22. %H A245290 Chai Wah Wu, <a href="http://arxiv.org/abs/1407.5663">Graphs whose normalized Laplacian matrices are separable as density matrices in quantum mechanics</a>, arXiv:1407.5663 [quant-ph], 2014. %F A245290 a(n) + A245291(n) = 2^(n*(2*n-1))-1. %F A245290 a(n) = 2^(n*(n-1))*A229865(n)-1. %Y A245290 Cf. A245291, A229865. %K A245290 nonn %O A245290 1,2 %A A245290 _Chai Wah Wu_, Jul 16 2014